Earthquake Warning Systems (EWS) rely on rapid detection and characterization of earthquake ground motions to provide alerts in advance of hazardous shaking. Most present EWS are designed to detect the start of an earthquake by sensing the arrival of P-waves and analyzing the P-wave to estimate the magnitude of the ongoing event via an empirical relationship between some property of the P-wave and the magnitude of historic earthquakes. The P-wave arrival times at several stations are used to estimate the event's epicenter. The estimated magnitude and epicenter are then used to estimate the intensity of impending ground motions, using an empirical relationship between magnitude, epicentral distance and intensity of ground motion. The amount of warning a P-wave based EWS can provide is proportional to the distance from the epicenter. A general rule of thumb is 1 second for every 8 km.
This technique leads to a multiplication of uncertainties between the estimation of magnitude from P-waves and intensity from the magnitude. In addition, time is of the essence in earthquake warnings, and this two-step estimation increases the computation time unnecessarily. The measurement uncertainty in the estimate is typically not reported along with the estimate itself, leading to a discontinuous response behavior in which a slight change in estimated ground motion leads to a drastically different response due to a particular threshold having been exceeded. For example, say an alarm is to be sounded for an estimated intensity of 5 or greater in some arbitrary scale. Without reporting the uncertainty in the estimate, the response for an estimated intensity of 4.999 is drastically different from the response for an estimated intensity of 5.000. In the latter case the alarm is sounded whereas in the former case, for a very similar ground motion estimate, no alarm is sounded. If, however, if the two estimated intensities are statistically indistinguishable because of their respective error ranges, the warning or other response to the estimates should not differ.
Other EWS rely on the detection of the S-wave at a sufficient distance to provide warning of intense shock waves. The amount of warning time possible is less, since the S-waves travel more slowly than P-waves, but some of the uncertainty in the estimate of intensity is reduced by waiting to directly measure the S-waves. This approach works best when likely epicenters are sufficiently far from population centers to provide time for remote sensors to wait for the S-wave and still be able to provide useful warning. Such a system warns Mexico City of earthquakes originating on the coast.
EWS designs are varied, but can be generally characterized as standalone or networked. A standalone EWS uses local sensing devices to make a strictly local decision about whether or not an earthquake has started and whether or not it is of sufficient intensity to justify the initiation of protective actions. These systems can react quickly to the arrival of a P-wave but may suffer from questionable false positive performance. A standalone device that relies on S-wave detection is normally called a seismic switch. These provide no warning of the earthquake, since they respond only after serious shaking begins, but can initiate actions that may prevent damage.
A networked EWS comprises geographically dispersed sites placed to minimize the distance to likely earthquake epicenters near likely epicenters. When an earthquake occurs, the P-waves travel outwards arriving first at the closest site which then sends a signal to all other affected sites. The warning time that the EWS can provide is better than the warning time possible with each standalone site, since the signal from the closest site will arrive at the other sites well before the arrival of the P-waves.
The normal warning time for a standalone system is given by the equation:twarn-standalone=ts−tp Where ts is the travel time for the S-wave from the hypocenter to the site and tp is the travel time for the P-wave from the hypocenter to the site. These travel times are:
                              t          s                =                  d                      V            S                                                            t          p                =                  d                      V            p                              Where d is the distance from the hypocenter to the site, Vs is the S-wave velocity, and Vp is the P-wave velocity. For a Poisson solid (a good approximation for the characteristics of the earth's crust):
            V      p              V      S        =      3  The time needed for the P-waves to arrive at the first sensor site is:
      t    F    =            d      F              V      p      Where tF is the travel time of the P-wave from the hypocenter to the first sensor site and dF is the distance from the hypocenter to the first sensor site. The warning time for the networked EWS (neglecting processing and communications delays) is:twarn-EWS=tS−tF 
The improvement in warning is:
  improvement  =                    t                  warn          -          EWS                            t                  warn          -          standalone                      =                                        t            S                    -                      t            F                                                              t              S                        -                          t              p                                ⁢                                                    =                                                  d                              V                S                                      -                                          d                F                                            V                p                                                                        d                              V                S                                      -                          d                              V                p                                                    =                                            3                        -                                          d                F                            d                                                          3              -              1                                          
When the first sensor site is located at the epicenter (dF=0, neglecting depth), the improvement ratio is:improvement=2.4
An improvement on the order of 2.4 is not generally considered possible in practice because of various system delays and hypocenter depths that were neglected in the above analysis. However, there can still be significant improvement, which is one reason that a networked EWS is a favored architecture.
In standard EWS systems, there are many sources of false positives caused by factors such as algorithm errors, electrical noise, mischief, or component failures, but the most common source of false positives is cultural noise: man-made vibrations that are difficult to distinguish from seismic events or that confuse seismic analysis algorithms. Reducing false positive probability by waiting for multiple sites to report trades warning time for reliability.
A networked EWS can potentially provide better false positive performance than a standalone EWS. To address the problem of false positives, a decision to distribute the warning can be postponed until several sites report the earthquake. The more sites reporting an earthquake, the more confidence there is in initiating costly actions. The time spent waiting for multiple sites, however, reduces the time available for completing protective actions; time that may be of significant value in protecting lives and reducing asset loss. However, if the reliability and confidence made possible by waiting for multiple sites to report could be achieved with only a single site, the performance of the EWS would be enhanced, helping get closer to that 2.4 improvement ratio.
The value of an EWS is measured by its ability to reduce injuries and protect assets from damage. A reliable EWS, one that avoids false positives and responds quickly to provide as much time as possible for completing protective actions, would be of significant value to those exposed to earthquake hazards.